Constant curvature foliations of Minkowski spacetimes with particles

Constant mean curvature (CMC) and constant sectional curvature hypersurfaces in $n$-dimensional ($n\geq 3$) Lorentzian manifolds (also called spacetimes) play an important role in pseudo-Riemannian geometry and general relativity.

Here we focus on the 3-dimensional case. It was shown by Barbot, B$\acute{e}$guin and Zeghib that every 3-dimensional GHMC (globally hyperbolic maximal compact) Minkowski spacetime admits a unique CMC foliation and a unique CGC (constant Gauss curvature) foliation.

In this talk, we are interested in the singular case, that is, 3-dimensional convex GHM Minkowski spacetimes with particles (cone singularities of angles less than $\pi$ along time-like curves), which are used in the physics literature to model point particles in 3d gravity. We will show that the corresponding results still hold in the singular case, using a method different from the regular case and some tools of Teichmüller theory with cone singularities. This is joint work with Andrea Tamburelli.